Improving Upper and Lower Bounds on the Order of Large Graphs under Degree and Distance Constraints. Networks govern all aspects of society, including transportation networks, communication networks, computer networks and networks for the distribution of goods etc. - and the theoretical analysis of such networks has become a subject of fundamental importance. Networks can be modelled by graphs. This project will provide new theoretical results which will improve our knowledge of network topologi ....Improving Upper and Lower Bounds on the Order of Large Graphs under Degree and Distance Constraints. Networks govern all aspects of society, including transportation networks, communication networks, computer networks and networks for the distribution of goods etc. - and the theoretical analysis of such networks has become a subject of fundamental importance. Networks can be modelled by graphs. This project will provide new theoretical results which will improve our knowledge of network topologies. The new knowledge will then be utilised in the construction of large graphs with respect to given maximum degree and distance constraints.Read moreRead less
Discrete integrable systems. Discrete integrable systems are a fundamental generalisation of traditional integrable systems. This project, combining 5 world experts from 3 countries and 2 early career researchers, will expand and systematise this new interdisciplinary field, and will place Australia at the forefront of this intensive international activity.
When the ice melts: a new perspective on the causes of Quaternary glacial terminations. The project will assemble an unprecedented palaeoclimate time series extending back to 1.2 million years ago that will allow marine and ice core records to be placed onto an absolute time scale. This will allow testing of fundamental hypotheses on why the Earth's climate shifts from glacial to interglacial states, with flow-on effects to climate models.
Understanding the sources of secular stagnation. This project aims to examine why long-run projections of output, inflation, and interest rates have become lower for many economies in recent years resulting in a phenomenon often referred to as secular stagnation. The project intends to develop new econometric tools to account for sources of structural breaks and stochastic trends in order to quantify the roles of productivity growth, financial shocks, demographics, and inflation expectations in ....Understanding the sources of secular stagnation. This project aims to examine why long-run projections of output, inflation, and interest rates have become lower for many economies in recent years resulting in a phenomenon often referred to as secular stagnation. The project intends to develop new econometric tools to account for sources of structural breaks and stochastic trends in order to quantify the roles of productivity growth, financial shocks, demographics, and inflation expectations in driving secular stagnation. Expected outcomes include findings that will help guide macroeconomic policy responses to stagnation and new econometric tools that will support future applied research on changes in the behaviour of macroeconomic variables.Read moreRead less
Nowcasting and Interpreting the Australian Economy. This project aims to investigate methods for nowcasting and interpreting the Australian economy. This is determining the current state of the economy and the factors contributing to it.
This project expects to generate new knowledge on how unconventional, new, data sources and innovative methods can be used to in nowcasting and how the Australian economy can be modelled.
The expected outcomes include timely new indicators of the state of the ec ....Nowcasting and Interpreting the Australian Economy. This project aims to investigate methods for nowcasting and interpreting the Australian economy. This is determining the current state of the economy and the factors contributing to it.
This project expects to generate new knowledge on how unconventional, new, data sources and innovative methods can be used to in nowcasting and how the Australian economy can be modelled.
The expected outcomes include timely new indicators of the state of the economy, and the factors contributing to it. This should provide significant benefits through informing the conduct of Australian macroeconomic policy, as the appropriate policy response depends not only on knowing the current state of the economy but understanding the economic factors underlying it.
Read moreRead less
Analysis of Fiscal Policy Responses to Macroeconomic Conditions in Australia and the US using Real Time Data. This project investigates the evolution of Australian and US fiscal policy responses to macroeconomic conditions and examines the implications for future levels of public debt. A real time database of fiscal indicators will be constructed to capture information available to policymakers when making decisions. Econometric analysis of the data will involve a flexible approach that captures ....Analysis of Fiscal Policy Responses to Macroeconomic Conditions in Australia and the US using Real Time Data. This project investigates the evolution of Australian and US fiscal policy responses to macroeconomic conditions and examines the implications for future levels of public debt. A real time database of fiscal indicators will be constructed to capture information available to policymakers when making decisions. Econometric analysis of the data will involve a flexible approach that captures how policy has changed in its focus on economic stabilisation and fiscal sustainability. The analysis also allows for forecasts of public debt that take into account the interaction between policy and the economy. The results and methods will be useful in evaluating the stance of fiscal policy and its implications for the sustainability of public debt.Read moreRead less
Invariants, geometric and discrete structures on manifolds. This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the ....Invariants, geometric and discrete structures on manifolds. This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the first aim is to construct structures with good geometric properties on 3- and 4-manifolds, using triangulations. The second aim is to study combinatorial decompositions of n-manifolds, using our new technique of multisections and also searching for polyhedral metrics of non-positive curvature. The third aim is to connect quantum invariants and geometric structures, again using triangulations.Read moreRead less
Higher dimensional methods for algebras and dynamical systems. Australian researchers have pioneered recent research in combinatorial C*-algebras. We are now uniquely placed to capitalise on this situation to make significant connections with research in dynamical systems. This project will thus position Australian mathematics at the nexus of two important research areas.
Triangulations in dimensions 3 and 4: discrete and geometric structures. Recently there have been spectacular advances in understanding 3-dimensional spaces and the interaction between ideas in mathematical physics (quantum invariants) and such spaces. This project aims at practical methods for finding geometric structures and advancing our understanding of the information that physics is providing about these spaces.
Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we ....Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we will forge connections between the geometry of curved spaces, and the physics of operators therein. The significant benefits of this project include increasing fundamental mathematical knowledge, building capacity in Australia’s world-class geometric analysis community, and strong links with international partners.Read moreRead less